Thanks, Merlin, for the information on Beyond Self-Interest and the particular paper in it by Virginia Held: “Mothering versus Contract.” I imagine it would be worthwhile to compare and assimilate Held’s ideas with Kathleen Touchstone’s Then Athena Said.

Oh, I see now that someone else noticed the connection to Prof. Touchstone’s book and mentioned it in a comment in your blog. Thanks for sharing the link there to Objectivity Archive. By the way, a year or two ago, Kathleen mentioned to me that she is working on another book. I don’t know the topic or the schedule.

Share this post

Link to post

Share on other sites

There is a review of Kathleen Touchstone’sThen Athena Said in The Journal of Ayn Rand Studies 8.2 (link). Since it is more than 5 years old, it can be read online for free with a JSTOR account, which can also be had for free.

That is the fallacy of asserting the consequent. which says if a implies b and b is asserted then a follows.

if you construct a truth table for ((a => b) & b) => a you will see the expression is not a tautology hence is not a valid inference form.

"=>" stands for implies and "&" for "and"

The algebraic logic formulated by George Boole in 1850 includes Aristotle's syllogistic as a special case. Way back when, Aristotle developed syllogistic categorical logic and the Stoics developed logic based on conditionals. The Stoic logic invented by Crysypus is mostly lost and the syllogistic logic based on categorical statements survived and was not improved upon until Leibniz attempted to reformulate logic (he was a bit ahead of his time) and George Boole and Gotleib Frege succeeded in the 19 th century. It was Boole's formulation of conditional logic what was applicable to expressing the logic of electronic computing machines.

Aristotle's syllogistic was correct as far as it went, but it could not handle binary relations well. Consider If all tigers are animals then the tail of a tiger is the tail of an animal. Or if x is the tail of a tiger then x is the tail of an animal. The binary relation x is the tail of y is no expressible in categorical form. The best one can do is all lion's tails are animal tail's therefore if x is a lion's tail then x is an animal's tail which is a conditional statement. The categorical version is all lion's tails are animal's tails. which does not follow from all lions are animals in the Aristotelian syllogistic. There is nothing wrong with Aristotle's logic but it is inflexible and somewhat constipated.

One wonders if the work of the Stoic school has survived long enough to be taken into the Islamic domains could it have migrated back into Europe in the late middle ages? The only reason that Aristotle's work even partially survived is that much of it was taken up by Islamic scholars and part of the Ulima (Muslim learning) and migrated back into Europe (the Byzantine empire) when Christian scholars when to the Muslim world to learn and thing or two. It was the Ulima that kept much of Greek thinking alive until middle ages in Europe. A great deal was lost when Julius Caesar burned down the library at Alexandria and later on the Christians burned what was not burned by Caesar.

Share this post

Link to post

Share on other sites

Aristotle's syllogistic was correct as far as it went, but it could not handle binary relations well. Consider If all tigers are animals then the tail of a tiger is the tail of an animal. Or if x is the tail of a tiger then x is the tail of an animal. The binary relation x is the tail of y is no expressible in categorical form.

You sound like a broken record, and Fred Sommers' term logic handles binary (and higher) relations very well.

You sound like a broken record, and Fred Sommers' term logic handles binary (and higher) relations very well.

Sommers and Engleburtsen had to -extend- the logic. Aristotle was nowhere near what they did. And even with term logic extended, term logic yields no useful metamathematical results. Goedel could not have proved the incompleteness theorems using term logic and term logic does not lend itself well to mathematical extension. Logic stagnated until Boole and Frege made the breakthrough by going back to Stoic conditional logic.

In logic design of circuits (necessary to get minimal circuits) Sommers-Engelburtsen term logic is nowhere used. S and E were very clever and original, but their term logic does not lend itself very well to computer execution. The programming language PROLOG and others are derived from first order logic. Set theory was finally nailed down by being basted on conditional logic. Term Logic bore no mathematical fruit. First and Higher order Predicate Logic did.

Computerization of grammar and machine translation were derived logically from the extensions of predicate logic. Next time you use Google Translate be aware there is a lot of mathematically based logic behind it.

It's written as a categorical syllogism, one that has a distribution error.

And I showed its conditional counterpart. Anything in categorical logic can be handled by conditional logic, in particular first order predicate logic. The converse, however, is not true. One of the reasons why modern predicate logic was developed was to handled binary and higher order relations flexibly.

Conditional logic was originated by the Stoics about the same time Aristotle operated his Lyceum. Crysippus, the Stoic was said to have write dozens, possibly hundreds of books on logic, but none of them have survived to this day. We only have fragmentary references to Stoic conditional logic by other writers, but the full details are lost in time. We are fortunate to have what we have of Aristotle. Some of his works were preserved by the Roman Cicero, others of his works somehow got to the Islamic domains where they become a hit and were carefully studied and expanded upon. In Europe, the study of logic mostly stagnated until the late middle ages when they returned to Europe. R. Maimonodes used Aristotle's logic to defend Judaism against Islam and a century later Thomas Acquinas used Aristotle's work to expound Catholicism.

Interesting, I went into solving #1 cold, without any further context. I got the right answer, then went on to #2 and the Wiki article. The method I used was System 1 according to the description, but when validating it I found my own answer was incorrect, then I came to the right answer, so I this was System 2 according to the description. All this took about 1 to 1.5min..

(Pats Self on back )

Share this post

Link to post

Share on other sites

I just looked at the problem and decided (spoiler alert) saved the most fuel without doing any calculation to speak of. I think the problem is set up to trap you in what seems obvious so I went with what I thought was the un-obvious answer. I also don't think it's close or the idea is you must do several detailed calculations and that shouldn't be what the author's about. If it's thinking fast and slow I did the fast for it took about 20 seconds. Still thinking about it as I write this if it's roughly three times the gas mileage the more economical vehicle uses, so 1/3 the fuel which magnifies the savings of the 12 - 14.

Now I'll try the second. My answer was correct. For 10,000 miles driving each, 12 - 14 saved roughly 36 gals over the 30 - 40. I took a lot of time before my young teenager arithmetic came back on line, however.